CN117497102B - Prediction method and system for helium bubble evolution of metal material irradiation - Google Patents
Prediction method and system for helium bubble evolution of metal material irradiation Download PDFInfo
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- SWQJXJOGLNCZEY-UHFFFAOYSA-N helium atom Chemical compound [He] SWQJXJOGLNCZEY-UHFFFAOYSA-N 0.000 title claims abstract description 167
- 229910052734 helium Inorganic materials 0.000 title claims abstract description 155
- 239000001307 helium Substances 0.000 title claims abstract description 141
- 238000000034 method Methods 0.000 title claims abstract description 49
- 239000007769 metal material Substances 0.000 title claims description 17
- 239000000463 material Substances 0.000 claims abstract description 70
- 239000000126 substance Substances 0.000 claims abstract description 25
- 239000007789 gas Substances 0.000 claims abstract description 13
- 239000002184 metal Substances 0.000 claims abstract description 10
- 229910052751 metal Inorganic materials 0.000 claims abstract description 10
- 230000015572 biosynthetic process Effects 0.000 claims description 38
- 238000004364 calculation method Methods 0.000 claims description 32
- 230000008569 process Effects 0.000 claims description 30
- 238000000329 molecular dynamics simulation Methods 0.000 claims description 14
- 239000011159 matrix material Substances 0.000 claims description 6
- 239000002245 particle Substances 0.000 claims description 6
- 230000000877 morphologic effect Effects 0.000 claims description 5
- 230000005855 radiation Effects 0.000 claims description 4
- 230000035945 sensitivity Effects 0.000 claims description 4
- 239000000203 mixture Substances 0.000 claims description 2
- 238000009792 diffusion process Methods 0.000 abstract description 5
- 230000035882 stress Effects 0.000 description 22
- 238000004088 simulation Methods 0.000 description 14
- 238000010586 diagram Methods 0.000 description 10
- 238000005457 optimization Methods 0.000 description 8
- 238000005516 engineering process Methods 0.000 description 5
- 229910000963 austenitic stainless steel Inorganic materials 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- -1 helium ions Chemical class 0.000 description 4
- 230000037230 mobility Effects 0.000 description 4
- 238000012545 processing Methods 0.000 description 4
- 238000004590 computer program Methods 0.000 description 3
- 230000007547 defect Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 238000005510 radiation hardening Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 101001121408 Homo sapiens L-amino-acid oxidase Proteins 0.000 description 2
- 102100026388 L-amino-acid oxidase Human genes 0.000 description 2
- 108010063499 Sigma Factor Proteins 0.000 description 2
- 238000005094 computer simulation Methods 0.000 description 2
- 125000004122 cyclic group Chemical group 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000009826 distribution Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
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- 101100012902 Saccharomyces cerevisiae (strain ATCC 204508 / S288c) FIG2 gene Proteins 0.000 description 1
- 238000005134 atomistic simulation Methods 0.000 description 1
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Abstract
Description
技术领域Technical Field
本发明涉及核电系统金属结构材料辐照条件下微观组织预测技术领域，具体而言，涉及一种用于金属材料辐照氦泡演化的预测方法及系统。The present invention relates to the technical field of microstructure prediction of metal structural materials in nuclear power systems under irradiation conditions, and in particular to a prediction method and system for helium bubble evolution in irradiated metal materials.
背景技术Background technique
随着现代社会对清洁能源的需求日益提升，核能已经称为现代能源体系的重要布局。以快中子增殖堆为主的先进核能系统的材料问题是项目发展的重点问题。核能的结构材料相比其他行业来说，其在服役过程中面临着中子辐照，持续的位移损伤会产生饱和点缺陷，如空位和间隙原子。在扩散、温度、应力和固有微结构(如晶界、位错和界面)的共同作用下，这些点缺陷往往会演变成位错环、空隙和气泡。由于辐照硬化和高温氦脆会导致金属晶间断裂，因此辐照材料中的嬗变氦形成的氦泡一直是特别关注的问题。然而，试验仪器空间和时间分辨率严重限制纳米和微米尺度的氦气泡研究。随着计算机模拟技术的发展，许多研究工作从原子尺度、纳米尺度和微观尺度揭示了He气泡的成核、生长和粗化过程，提高了对辐照材料中He泡的理解。但实际服役过程中He泡的演化和材料的应力应变状态有着强烈的交互作用。一方面，He泡内部的高压可能会导致高温下的塑性变形，从未在服役条件下材料发生屈服。另一方面，核电结构材料往往在应力作用下服役，但少有研究报道了应力状态对辐照He泡的影响。因此，建立具有物理意义的He泡演化方程对理解辐照He泡的形成以及预测材料中的辐照缺陷具有重要意义，从而深入理解辐照He泡和应力状态之间的交互作用，可以为进行核电结构材料性能评价和寿命预测提供重要的理论依据。With the increasing demand for clean energy in modern society, nuclear energy has become an important layout of the modern energy system. The material problem of advanced nuclear energy systems based on fast neutron breeder reactors is a key issue in project development. Compared with other industries, nuclear energy structural materials are exposed to neutron irradiation during service, and continuous displacement damage will produce saturated point defects such as vacancies and interstitial atoms. Under the combined effects of diffusion, temperature, stress and inherent microstructure (such as grain boundaries, dislocations and interfaces), these point defects often evolve into dislocation loops, voids and bubbles. Since radiation hardening and high-temperature helium embrittlement can cause intergranular fracture of metals, helium bubbles formed by transmuted helium in irradiated materials have always been a special concern. However, the spatial and temporal resolution of experimental instruments severely limits the study of helium bubbles at the nano and micro scales. With the development of computer simulation technology, many research works have revealed the nucleation, growth and coarsening processes of He bubbles from the atomic, nano and micro scales, improving the understanding of He bubbles in irradiated materials. However, the evolution of He bubbles in actual service has a strong interaction with the stress-strain state of the material. On the one hand, the high pressure inside the He bubble may cause plastic deformation at high temperature, and the material has never yielded under service conditions. On the other hand, nuclear power structural materials often serve under stress, but few studies have reported the effect of stress state on irradiated He bubbles. Therefore, establishing a physically meaningful He bubble evolution equation is of great significance for understanding the formation of irradiated He bubbles and predicting irradiation defects in materials. In-depth understanding of the interaction between irradiated He bubbles and stress state can provide an important theoretical basis for performance evaluation and life prediction of nuclear power structural materials.
发明内容Summary of the invention
为了解决上述问题，本发明的目的是提供一种定量预测氦泡演化的技术，为更加机理化地在辐照条件下氦泡演化奠定理论基础。In order to solve the above problems, the purpose of the present invention is to provide a technology for quantitatively predicting the evolution of helium bubbles, so as to lay a theoretical foundation for a more mechanistic evolution of helium bubbles under irradiation conditions.
为了实现上述技术目的，本申请提供了一种用于金属材料辐照氦泡演化的预测方法，包括以下步骤：In order to achieve the above technical objectives, the present application provides a method for predicting the evolution of helium bubbles in metal materials irradiated with radiation, comprising the following steps:
基于核电结构材料的空位形成能、氦原子形成能、气体常数、摩尔体积分数以及绝对温度，获取核电结构材料的化学自由能密度；Obtain the chemical free energy density of nuclear power structural materials based on vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction and absolute temperature of nuclear power structural materials;
基于核电结构材料的弹性常数以及弹性应变，获取核电结构材料的弹性自由能密度；Based on the elastic constants and elastic strains of nuclear power structural materials, the elastic free energy density of nuclear power structural materials is obtained;
基于化学自由能密度和弹性自由能密度，通过采集核电结构材料的空位和氦原子的扩散系数，以及辐照氦原子的产生速率，构建基于相场方程的动力学模型，对核电结构材料的辐照氦泡演化进行预测。Based on the chemical free energy density and elastic free energy density, by collecting the diffusion coefficients of vacancies and helium atoms in nuclear power structural materials, as well as the production rate of irradiated helium atoms, a kinetic model based on the phase field equation is constructed to predict the evolution of irradiated helium bubbles in nuclear power structural materials.
优选地，在获取核电结构材料的空位形成能和氦原子形成能的过程中，通过获取优化后含有空位的晶胞总能量和优化后含有间隙氦原子的晶胞总能量，根据优化后完整晶胞的总能量和总的粒子数，进行分子动力学计算，分别获取空位形成能和氦原子形成能。Preferably, in the process of obtaining the vacancy formation energy and helium atom formation energy of nuclear power structural materials, the total energy of the optimized unit cell containing vacancies and the total energy of the optimized unit cell containing interstitial helium atoms are obtained, and molecular dynamics calculations are performed based on the total energy and total number of particles of the optimized complete unit cell to obtain the vacancy formation energy and helium atom formation energy, respectively.
优选地，在获取化学自由能密度的过程中，基于基体的第一自由能密度和氦泡的第二自由能密度，通过设置插值函数，生成化学自由能密度，其中，根据空位浓度和氦浓度，获取第一自由能密度和第二自由能密度。Preferably, in the process of obtaining the chemical free energy density, the chemical free energy density is generated by setting an interpolation function based on the first free energy density of the matrix and the second free energy density of the helium bubbles, wherein the first free energy density and the second free energy density are obtained according to the vacancy concentration and the helium concentration.
优选地，在获取第一自由能密度的过程中，基于空位浓度和氦浓度，根据摩尔体积分数、阿伏伽德罗常数、气体常数和绝对温度，获取第一自由能密度。Preferably, in the process of obtaining the first free energy density, the first free energy density is obtained based on the vacancy concentration and the helium concentration, according to the molar volume fraction, the Avogadro constant, the gas constant and the absolute temperature.
优选地，在获取第二自由能密度的过程中，基于空位浓度和氦浓度，根据氦泡中氦的平衡浓度，以及氦泡中氦的最大浓度，并依据摩尔体积分数、气体常数和绝对温度，获取第二自由能密度。Preferably, in the process of obtaining the second free energy density, the second free energy density is obtained based on the vacancy concentration and the helium concentration, according to the equilibrium concentration of helium in the helium bubbles, and the maximum concentration of helium in the helium bubbles, and according to the molar volume fraction, the gas constant and the absolute temperature.
优选地，在获取弹性常数和弹性应变的过程中，通过获取核电结构材料的j方向上的小应变、正应变条件下的应力和负应变条件下的应力，获取核电结构材料的弹性常数；Preferably, in the process of obtaining the elastic constant and the elastic strain, the elastic constant of the nuclear power structure material is obtained by obtaining the small strain in the j direction of the nuclear power structure material, the stress under the positive strain condition, and the stress under the negative strain condition;
基于核电结构材料的总应变，根据核电结构材料的辐照氦泡的本征应变，以及核电结构材料的塑性应变，获取弹性应变。Based on the total strain of the nuclear power structural material, the elastic strain is obtained according to the intrinsic strain of the irradiated helium bubble of the nuclear power structural material and the plastic strain of the nuclear power structural material.
优选地，在获取辐照氦泡的本征应变的过程中，通过获取氦泡内压和弹性常数的分量，依据克罗内克函数，获取辐照氦泡的本征应变，其中，通过氦泡内氦浓度、玻尔兹曼常数、绝对温度、原子体积和范德瓦尔斯常数，获取氦泡内压。Preferably, in the process of obtaining the intrinsic strain of the irradiated helium bubble, the intrinsic strain of the irradiated helium bubble is obtained by obtaining the components of the internal pressure of the helium bubble and the elastic constant according to the Kronecker function, wherein the internal pressure of the helium bubble is obtained by the helium concentration in the helium bubble, the Boltzmann constant, the absolute temperature, the atomic volume and the van der Waals constant.
优选地，在获取塑性应变的过程中，根据初始塑性剪切率、位错的剪切率、应变敏感指数、Schimid张量因子、应力张量、临界剪切应力、总的滑移系数量和当前滑移系，获取塑性应变。Preferably, in the process of obtaining the plastic strain, the plastic strain is obtained according to the initial plastic shear rate, the shear rate of the dislocation, the strain sensitivity index, the Schimid tensor factor, the stress tensor, the critical shear stress, the total number of slip systems and the current slip system.
优选地，在对核电结构材料的辐照氦泡演化进行预测的过程中，基于化学自由能密度和弹性自由能密度，构建描述核电系统金属结构材料辐照氦泡演化的相场方程热力学模型；通过获取界面迁移率、氦以及空位的化学迁移率和辐照条件下氦以及空位的产生速率，构建相场方程的动力学模型，获取当前时间步的成分场和序参数场，进行可视化，获取当前时间步氦泡的形貌演化，并根据序参数场对氦泡密度以及尺寸进行定量统计后，进行迭代计算，获得辐照氦泡的演化过程。Preferably, in the process of predicting the evolution of irradiated helium bubbles of nuclear power structural materials, a phase field equation thermodynamic model describing the evolution of irradiated helium bubbles of metal structural materials of nuclear power systems is constructed based on chemical free energy density and elastic free energy density; a kinetic model of the phase field equation is constructed by obtaining interface mobility, chemical mobility of helium and vacancies, and the generation rate of helium and vacancies under irradiation conditions, and the component field and order parameter field of the current time step are obtained and visualized to obtain the morphological evolution of the helium bubbles in the current time step, and after quantitative statistics of the density and size of the helium bubbles according to the order parameter field, iterative calculation is performed to obtain the evolution process of the irradiated helium bubbles.
本发明还公开了一种用于金属材料辐照氦泡演化的预测系统，包括：The present invention also discloses a prediction system for the evolution of helium bubbles irradiated by metal materials, comprising:
数据采集模块，用于采集核电结构材料的空位形成能、氦原子形成能、气体常数、摩尔体积分数以及绝对温度；Data acquisition module, used to collect vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction and absolute temperature of nuclear power structural materials;
化学自由能密度计算模块，用于根据核电结构材料的空位形成能、氦原子形成能、气体常数、摩尔体积分数以及绝对温度。获取核电结构材料的化学自由能密度；The chemical free energy density calculation module is used to obtain the chemical free energy density of nuclear power structural materials based on the vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction and absolute temperature of nuclear power structural materials;
弹性自由能密度计算模块，用于基于核电结构材料的弹性常数以及弹性应变，获取核电结构材料的弹性自由能密度；Elastic free energy density calculation module, used to obtain the elastic free energy density of nuclear power structural materials based on the elastic constants and elastic strains of nuclear power structural materials;
辐照氦泡演化预测模块，用于基于化学自由能密度和弹性自由能密度，构建描述核电系统金属结构材料辐照氦泡演化的相场方程的热力学模型；通过采集核电结构材料的空位和氦原子的扩散系数，以及辐照氦原子的产生速率，构建相场方程的动力学模型，对核电结构材料的辐照氦泡演化进行预测。The irradiated helium bubble evolution prediction module is used to construct a thermodynamic model of the phase field equation that describes the evolution of irradiated helium bubbles in metal structural materials of nuclear power systems based on chemical free energy density and elastic free energy density. By collecting the diffusion coefficients of vacancies and helium atoms in nuclear power structural materials, as well as the generation rate of irradiated helium atoms, a kinetic model of the phase field equation is constructed to predict the evolution of irradiated helium bubbles in nuclear power structural materials.
本发明公开了以下技术效果：The present invention discloses the following technical effects:
本发明利用相场模拟可以研究辐照氦泡的形成及演化，定量化得出氦泡的密度以及尺寸，可以有限弥补实验研究的不足；The present invention can study the formation and evolution of irradiated helium bubbles by using phase field simulation, and quantitatively obtain the density and size of helium bubbles, which can make up for the shortcomings of experimental research to a limited extent.
本发明基于晶体塑性理论，考虑了氦泡内的高内压可能引起的塑性变形，提高了相场模拟预测氦泡演化的精度；The present invention is based on the crystal plasticity theory, takes into account the plastic deformation that may be caused by the high internal pressure in the helium bubble, and improves the accuracy of phase field simulation in predicting the evolution of the helium bubble;
本发明提到的预测方法简单，所需要的参数可以通过原子模拟以及有限元模拟确定。The prediction method mentioned in the present invention is simple, and the required parameters can be determined through atomistic simulation and finite element simulation.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
图1是本发明实施例所述的方法流程示意图；FIG1 is a schematic diagram of a method flow chart of an embodiment of the present invention;
图2是本发明实施例所述的模拟单个氦泡的演化过程图，其中，a图为模拟步为1，b图为模拟时间步20，c图为模拟时间步30。；FIG2 is a diagram of the evolution process of simulating a single helium bubble according to an embodiment of the present invention, wherein FIGa is a simulation step of 1, FIGb is a simulation time step of 20, and FIGc is a simulation time step of 30. ;
图3是本发明实施例所述的模拟单个氦泡演化过程中氦浓度的变化示意图；3 is a schematic diagram of changes in helium concentration during the simulation of the evolution of a single helium bubble according to an embodiment of the present invention;
图4是本发明实施例所述的模拟316H奥氏体不锈钢550℃氦离子辐照条件下氦泡的尺寸以及尺寸分布与实验的对比图；4 is a comparison diagram of the size and size distribution of helium bubbles under the conditions of simulating 316H austenitic stainless steel irradiated with helium ions at 550° C. according to an embodiment of the present invention and an experiment;
图5是本发明实施例所述的模拟316H奥氏体不锈钢550℃氦离子辐照条件下应力作用对He泡的影响。FIG. 5 is a diagram showing the effect of stress on He bubbles under conditions of 550° C. helium ion irradiation of simulated 316H austenitic stainless steel according to an embodiment of the present invention.
具体实施方式Detailed ways
为使本申请实施例的目的、技术方案和优点更加清楚，下面将结合本申请实施例中附图，对本申请实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本申请一部分实施例，而不是全部的实施例。通常在此处附图中描述和示出的本申请实施例的组件可以以各种不同的配置来布置和设计。因此，以下对在附图中提供的本申请的实施例的详细描述并非旨在限制要求保护的本申请的范围，而是仅仅表示本申请的选定实施例。基于本申请的实施例，本领域技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例，都属于本申请保护的范围。To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application usually described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.
如图1-5所示，本发明提供了一种用于金属材料辐照氦泡演化的预测技术，包括预测方法，以及根据预测方法构建预测系统的过程，具体过程如下：As shown in FIGS. 1-5 , the present invention provides a prediction technology for the evolution of helium bubbles in metal materials irradiated with radiation, including a prediction method and a process of constructing a prediction system according to the prediction method. The specific process is as follows:
基于核电结构材料的空位形成能、氦原子形成能、气体常数、摩尔体积分数以及绝对温度，建立材料的化学自由能密度；The chemical free energy density of nuclear power structural materials is established based on the vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction and absolute temperature;
基于核电结构材料的弹性常数以及弹性应变，建立材料的弹性自由能密度；Based on the elastic constants and elastic strains of nuclear power structural materials, the elastic free energy density of the materials is established;
基于化学自由能密度以及弹性自由能密度，构建用于描述核电系统金属结构材料辐照氦泡演化的相场方程热力学(模型)模块；Based on the chemical free energy density and elastic free energy density, a phase field equation thermodynamics (model) module is constructed to describe the evolution of helium bubbles in irradiated metal structural materials of nuclear power systems.
基于热力学(模型)模块，通过采集核电结构材料的空位以及氦原子的扩散系数以及辐照氦原子的产生速率，构建相场方程的动力学(模型)模块；Based on the thermodynamics (model) module, the dynamics (model) module of the phase field equation is constructed by collecting the vacancies of nuclear power structural materials, the diffusion coefficient of helium atoms, and the generation rate of irradiated helium atoms;
基于相场动力学(模型)模块的计算结果，建立数据处理(模型)模块。Based on the calculation results of the phase field dynamics (model) module, a data processing (model) module is established.
基于数据处理(模型)模块的数据结果，进行下一个模拟时间步的热力学(模型)模块和动力学(模型)模块的计算，以此循环迭代获取辐照氦泡的演化。Based on the data results of the data processing (model) module, the thermodynamic (model) module and the kinetic (model) module are calculated for the next simulation time step, so as to obtain the evolution of the irradiated helium bubble through iterative cycles.
空位形成能以及氦原子形成能是基于分子动力学计算的。The vacancy formation energies and helium atom formation energies are calculated based on molecular dynamics.
分子动力学计算方法为：采用LAMMPS软件进行分子动力学计算，空位形成能的计算公式为：The molecular dynamics calculation method is: LAMMPS software is used for molecular dynamics calculation, and the calculation formula of vacancy formation energy is:
式中，为空位形成能，Ef为优化后含有空位的晶胞总能量，E0为优化后完整晶胞的总能量，N0为总的粒子数。In the formula, is the vacancy formation energy, Ef is the total energy of the unit cell containing vacancies after optimization, E0 is the total energy of the complete unit cell after optimization, and N0 is the total number of particles.
氦原子的形成能的计算公式为：The calculation formula for the formation energy of helium atoms is:
式中，为氦原子形成能，Ei为优化后含有间隙氦原子的晶胞总能量，E0为优化后完整晶胞的总能量，N0为总的粒子数。In the formula, is the formation energy of helium atoms, Ei is the total energy of the unit cell containing interstitial helium atoms after optimization, E0 is the total energy of the complete unit cell after optimization, and N0 is the total number of particles.
材料的弹性常数是基于分子动力学计算的。The elastic constants of the materials were calculated based on molecular dynamics.
分子动力学计算方法为：用LAMMPS软件进行分子动力学计算，弹性常数的计算公式为：The molecular dynamics calculation method is: molecular dynamics calculation is performed using LAMMPS software, and the elastic constant calculation formula is:
式中，Cij为弹性常数，δεj为j方向上的小应变，<σi(+δεj)>为正应变条件下的应力，<σi(-δεj)>为负应变条件下的应力。Where C ij is the elastic constant, δε j is the small strain in the j direction, <σ i (+δε j )> is the stress under positive strain conditions, and <σ i (-δε j )> is the stress under negative strain conditions.
弹性应变的计算公式为：The calculation formula for elastic strain is:
式中，为弹性应变，εij为总应变，为辐照氦泡的本征应变，为塑性应变。In the formula, is the elastic strain, ε ij is the total strain, is the intrinsic strain of the irradiated helium bubble, is the plastic strain.
辐照氦泡的本征应变计算公式为：The calculation formula of the intrinsic strain of irradiated helium bubble is:
式中，P为氦泡内压，C11和C12为弹性常数的分量，δij为克罗内克函数。Where P is the internal pressure of the helium bubble, C 11 and C 12 are the components of the elastic constants, and δ ij is the Kronecker function.
氦泡内压是基于氦泡内氦浓度计算的，计算公式为：The internal pressure of the helium bubble is calculated based on the helium concentration in the helium bubble. The calculation formula is:
式中，cg为氦泡内氦浓度，kB为玻尔兹曼常数，T为绝对温度，Ω为原子体积，b为范德瓦尔斯常数。Where cg is the helium concentration in the helium bubble, kB is the Boltzmann constant, T is the absolute temperature, Ω is the atomic volume, and b is the van der Waals constant.
塑性应变的计算公式为：The calculation formula for plastic strain is:
式中，为初始塑性剪切率，为位错的剪切率，n为应变敏感指数，mα为Schimid张量因子，σ为应力张量，为临界剪切应力，N为总的滑移系数量，α为当前滑移系。In the formula, is the initial plastic shear rate, is the shear rate of dislocation, n is the strain sensitivity index, m α is the Schimid tensor factor, σ is the stress tensor, is the critical shear stress, N is the total number of slip systems, and α is the current slip system.
临界剪切应力是基于位错模型计算的，其计算公式为：The critical shear stress is calculated based on the dislocation model, and its calculation formula is:
式中，为晶格固有阻力，为可动位错密度，为不可动位错密度，aα为位错之间的硬化系数，μ为剪切模量，b为柏氏矢量的长度，Δτir为辐照硬化对临界剪切应力的贡献。In the formula, is the lattice intrinsic resistance, is the mobile dislocation density, is the immobile dislocation density, a α is the hardening coefficient between dislocations, μ is the shear modulus, b is the length of the Burgers vector, and Δτ ir is the contribution of radiation hardening to the critical shear stress.
位错密度的计算公式为：The calculation formula for dislocation density is:
式中，kmul，Rcp,βρ，krecov分别表示可动位错的增殖，可动位错的湮灭，可动位错被阻碍和不可动位错的热回复。Where k mul , R cp , β ρ , and k recov represent the multiplication of mobile dislocations, the annihilation of mobile dislocations, the hindrance of mobile dislocations, and the thermal recovery of immobile dislocations, respectively.
基于相场方程的动力学(模型)模块计算所得的当前时间步的成分场和序参数场，采用PARAVIEW软件进行可视化，获得氦泡的形貌演化；The composition field and order parameter field of the current time step calculated by the dynamics (model) module based on the phase field equation are visualized using PARAVIEW software to obtain the morphological evolution of the helium bubble;
基于场方程的动力学(模型)模块计算所得的当前时间步的序参数场对氦泡密度以及尺寸进行定量统计。The order parameter field of the current time step calculated by the dynamics (model) module based on the field equations is used to quantitatively count the density and size of helium bubbles.
基于定量统计的氦泡密度以及尺寸，获取下一时间步的氦泡内压，进行循环迭代，获得辐照氦泡的演化过程。Based on the quantitative statistics of helium bubble density and size, the internal pressure of the helium bubble in the next time step is obtained, and the evolution process of the irradiated helium bubble is obtained by cyclic iteration.
实施例1：实施例采用本发明提供的一种金属材料辐照氦泡演化的预测技术，以核级316H奥氏体不锈钢为例，包括以下步骤：Example 1: The example adopts a prediction technology for the evolution of helium bubbles in metal materials irradiated by the present invention, taking nuclear grade 316H austenitic stainless steel as an example, and includes the following steps:
如图1所示，本说明书实施例提供的一种金属材料辐照氦泡演化的预测技术的流程示意图。As shown in FIG1 , a schematic diagram of a process of predicting the evolution of helium bubbles in metal materials irradiated with radiation is provided in an embodiment of this specification.
步骤1：基于分子动力学计算空位形成能以及氦原子形成能。Step 1: Calculate the vacancy formation energy and the helium atom formation energy based on molecular dynamics.
分子动力学计算方法为：采用LAMMPS软件进行分子动力学计算，空位形成能的计算公式为：The molecular dynamics calculation method is: LAMMPS software is used for molecular dynamics calculation, and the calculation formula of vacancy formation energy is:
式中，为空位形成能，Ef为优化后含有空位的晶胞总能量，E0为优化后完整晶胞的总能量，N0为总的粒子数。In the formula, is the vacancy formation energy, Ef is the total energy of the unit cell containing vacancies after optimization, E0 is the total energy of the complete unit cell after optimization, and N0 is the total number of particles.
氦原子的形成能的计算公式为：The calculation formula for the formation energy of helium atoms is:
式中，为氦原子形成能，Ei为优化后含有间隙氦原子的晶胞总能量，E0为优化后完整晶胞的总能量，N0为总的粒子数。In the formula, is the formation energy of helium atoms, Ei is the total energy of the unit cell containing interstitial helium atoms after optimization, E0 is the total energy of the complete unit cell after optimization, and N0 is the total number of particles.
步骤2：获取化学自由能密度：Step 2: Obtain the chemical free energy density:
fbulk＝h(η)fmatrix(cv,cg)+j(η)fbubble(cv,cg)； fbulk ＝h(η) fmatrix (c v ,c g )+j(η) fbubble (c v ,c g );
式中，h(η)＝(η-1)2和j(η)＝η2为插值函数，fmatrix和fbubble分别为基体的自由能密度(第一自由能密度)和氦泡的自由能密度(第二自由能密度)，cv和cg为相场模拟中成分场，分别表示空位浓度和氦浓度。η是相场模拟中描述氦泡演化的非保守场变量，η＝0表示基体，η＝1表示氦泡。Where, h(η) = (η-1) 2 and j(η) = η 2 are interpolation functions, f matrix and f bubble are the free energy density of the matrix (first free energy density) and the free energy density of the helium bubble (second free energy density), respectively, c v and c g are the component fields in the phase field simulation, representing the vacancy concentration and helium concentration, respectively. η is a non-conservative field variable describing the evolution of helium bubbles in the phase field simulation, η = 0 represents the matrix, and η = 1 represents the helium bubble.
基体的自由能密度的表达式为：The free energy density of the matrix is expressed as:
式中，Vm为摩尔体积分数，NA为阿伏伽德罗常数，R为气体常数，T为绝对温度。Where Vm is the molar volume fraction, NA is the Avogadro constant, R is the gas constant, and T is the absolute temperature.
氦泡的自由能密度表达式为：The free energy density of helium bubble is expressed as:
式中，为氦泡中氦的平衡浓度，为氦泡中氦的最大浓度。In the formula, is the equilibrium concentration of helium in the helium bubble, is the maximum concentration of helium in the helium bubble.
步骤3：基于分子动力学计算材料的弹性常数。分子动力学计算方法为：用LAMMPS软件进行分子动力学计算，弹性常数的计算公式为：Step 3: Calculate the elastic constants of the material based on molecular dynamics. The molecular dynamics calculation method is: use LAMMPS software to perform molecular dynamics calculations, and the calculation formula for the elastic constants is:
式中，Cij为弹性常数，δεj为j方向上的小应变，<σi(+δεj)>为正应变条件下的应力，<σi(-δεj)>为负应变条件下的应力。Where C ij is the elastic constant, δε j is the small strain in the j direction, <σ i (+δε j )> is the stress under positive strain conditions, and <σ i (-δε j )> is the stress under negative strain conditions.
步骤4：写出弹性应变计算公式：Step 4: Write the elastic strain calculation formula:
式中，为弹性应变，εij为总应变，为辐照氦泡的本征应变，为塑性应变。In the formula, is the elastic strain, ε ij is the total strain, is the intrinsic strain of the irradiated helium bubble, is the plastic strain.
步骤5：计算辐照氦泡的本征应变：Step 5: Calculate the intrinsic strain of the irradiated helium bubble:
式中，P为氦泡内压，C11和C12为弹性常数的分量，δij为克罗内克函数。Where P is the internal pressure of the helium bubble, C 11 and C 12 are the components of the elastic constants, and δ ij is the Kronecker function.
氦泡内压是基于氦泡内氦浓度计算的，计算公式为：The internal pressure of the helium bubble is calculated based on the helium concentration in the helium bubble. The calculation formula is:
式中，cg为氦泡内氦浓度，kB为玻尔兹曼常数，T为绝对温度，Ω为原子体积，b为范德瓦尔斯常数。Where cg is the helium concentration in the helium bubble, kB is the Boltzmann constant, T is the absolute temperature, Ω is the atomic volume, and b is the van der Waals constant.
步骤6：计算塑性应变：Step 6: Calculate plastic strain:
式中，为初始塑性剪切率，为位错的剪切率，n为应变敏感指数，mα为Schimid张量因子，σ为应力张量，为临界剪切应力，N为总的滑移系数量，α为当前滑移系。In the formula, is the initial plastic shear rate, is the shear rate of dislocation, n is the strain sensitivity index, m α is the Schimid tensor factor, σ is the stress tensor, is the critical shear stress, N is the total number of slip systems, and α is the current slip system.
在步骤6中，临界剪切应力的计算公式为：In step 6, the critical shear stress is calculated as:
式中，为晶格固有阻力，为可动位错密度，为不可动位错密度，aα为位错之间的硬化系数，μ为剪切模量，b为柏氏矢量的长度，Δτir为辐照硬化对临界剪切应力的贡献。In the formula, is the lattice intrinsic resistance, is the mobile dislocation density, is the immobile dislocation density, a α is the hardening coefficient between dislocations, μ is the shear modulus, b is the length of the Burgers vector, and Δτ ir is the contribution of radiation hardening to the critical shear stress.
在步骤6中，位错密度的计算公式为：In step 6, the dislocation density is calculated as:
式中，kmul，Rcp,βρ，krecov分别表示可动位错的增殖，可动位错的湮灭，可动位错被阻碍和不可动位错的热回复。Where k mul , R cp , β ρ , and k recov represent the multiplication of mobile dislocations, the annihilation of mobile dislocations, the hindrance of mobile dislocations, and the thermal recovery of immobile dislocations, respectively.
步骤7：基于所计算的氦泡的本征应变和塑性应变，获取弹性自由能密度：Step 7: Based on the calculated intrinsic strain and plastic strain of the helium bubble, obtain the elastic free energy density:
式中，Cijkl表示弹性常数，εij表示总应变，表示氦泡的本征应变，表示塑性应变。Where C ijkl represents the elastic constant, ε ij represents the total strain, represents the intrinsic strain of the helium bubble, represents the plastic strain.
步骤8：根据所计算的化学自由能密度以及弹性自由能密度构建用于描述核电系统金属结构材料辐照氦泡演化的相场方程热力学(模型)模块：Step 8: Based on the calculated chemical free energy density and elastic free energy density, a phase field equation thermodynamics (model) module is constructed to describe the evolution of helium bubbles in metal structural materials of nuclear power systems during irradiation:
式中，F表示整个模拟体系的能量，k为与界面能相关的参数，V代表相场模拟体系。Where F represents the energy of the entire simulation system, k is a parameter related to the interface energy, and V represents the phase field simulation system.
步骤9：构建相场方程的动力学(模型)模块：Step 9: Construct the dynamics (model) module of the phase field equation:
式中，Mη为界面迁移率，Mg和Mv为氦以及空位的化学迁移率，gg和gv表示辐照条件下氦以及空位的产生速率。Where M η is the interface mobility, Mg and Mv are the chemical mobilities of helium and vacancies, and g g and gv represent the generation rates of helium and vacancies under irradiation conditions.
步骤10：基于相场方程的动力学(模型)模块计算所得的当前时间步的成分场和序参数场，采用PARAVIEW软件进行可视化，获得当前时间步氦泡的形貌演化；基于场方程的动力学(模型)模块计算所得的当前时间步的序参数场对氦泡密度以及尺寸进行定量统计。Step 10: The component field and order parameter field of the current time step calculated by the dynamics (model) module based on the phase field equation are visualized using PARAVIEW software to obtain the morphological evolution of the helium bubble in the current time step; the order parameter field of the current time step calculated by the dynamics (model) module based on the field equation is used to quantitatively count the density and size of the helium bubble.
步骤11，基于步骤10中的密度以及尺寸，根据步骤5中的公式获取下一时间步的氦泡内压，进行循环迭代，获得辐照氦泡的演化过程。如表1所示，提供了实施例1的主要物性参数Step 11, based on the density and size in step 10, the internal pressure of the helium bubble in the next time step is obtained according to the formula in step 5, and the cyclic iteration is performed to obtain the evolution process of the irradiated helium bubble. As shown in Table 1, the main physical property parameters of Example 1 are provided.
表1Table 1
图4-5所示，利用本发明提供的金属材料辐照氦泡演化的预测技术模拟316H奥氏体不锈钢550℃条件下氦离子辐照条件下氦泡的尺寸以及尺寸分布与实验的对比，以及氦离子辐照条件下应力作用对He泡的影响，可以发现相场模拟具有较好的预测精度，以及外应力作用可以促进辐照He泡的形成，相场模拟可以弥补实验研究的不足。As shown in Figures 4-5, the prediction technology for the evolution of helium bubbles irradiated by metal materials provided by the present invention is used to simulate the size and size distribution of helium bubbles under helium ion irradiation conditions of 316H austenitic stainless steel at 550°C, and the comparison with the experiment, as well as the effect of stress on He bubbles under helium ion irradiation conditions, shows that phase field simulation has good prediction accuracy, and external stress can promote the formation of irradiated He bubbles. Phase field simulation can make up for the shortcomings of experimental research.
实施例结果表明，本发明预测辐照条件下氦泡的形成及演化，提供了一种定量预测氦泡演化的方法。这为更加机理化的辐照条件下氦泡演化奠定了理论基础，可以作为辐照条件下核电系统结构材料微观组织预测的理论基础，提高了计算模拟的应用价值。The results of the examples show that the present invention predicts the formation and evolution of helium bubbles under irradiation conditions, and provides a method for quantitatively predicting the evolution of helium bubbles. This lays a theoretical foundation for a more mechanistic evolution of helium bubbles under irradiation conditions, and can serve as a theoretical basis for predicting the microstructure of structural materials of nuclear power systems under irradiation conditions, thus improving the application value of computational simulation.
本发明是参照根据本发明实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present invention is described with reference to the flowchart and/or block diagram of the method, device (system), and computer program product according to the embodiment of the present invention. It should be understood that each process and/or box in the flowchart and/or block diagram, as well as the combination of the process and/or box in the flowchart and/or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
在本发明的描述中，需要理解的是，术语“第一”、“第二”仅用于描述目的，而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此，限定有“第一”、“第二”的特征可以明示或者隐含地包括一个或者更多个该特征。在本发明的描述中，“多个”的含义是两个或两个以上，除非另有明确具体的限定。In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.
显然，本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围。这样，倘若本发明的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.
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| CN113255136A (en) * | 2021-05-28 | 2021-08-13 | 大连理工大学 | Phase field simulation method and system for predicting irradiation bubble evolution |
| CN114283893A (en) * | 2021-12-22 | 2022-04-05 | 中北大学 | Simulation method for vacancy and interstitial atom defects in iron-copper-manganese-nickel quaternary alloy |
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